The Daily Star Sunday is increasing its cover price for the second time in a month, to 70p, after sales dipped below rival the People for the first time since the Sun on Sunday launched on 26 February.

Richard Desmond's Sunday red-top will rise from 60p to 70p on 29 July. This comes just over a month after the last 10p rise, to 60p, on 24 June.

The latest rise means the cost of the Daily Star Sunday has risen 40% in a matter of weeks.

However, this is still well below the Daily Star Sunday's £1 cover price up to late February, when the paper was cut to 50p to match the cost of the new Sunday edition of the Sun.

It appears that last month's rise has already started to affect sales, with the Daily Star Sunday selling a few thousand less than Trinity Mirror rival the People on Sunday, according to unofficial industry figures for last weekend.

The People, which sells for almost twice the price of the Daily Star Sunday at £1, sold about 468,000 copies on the weekend.

Desmond's title sold about 466,000, the first time it has shifted fewer copies than its rival since February.

The People has traditionally been more popular, selling about 474,000 copies before the closure of the News of the World, against about 306,000 a week for the Daily Star Sunday.

Both titles enjoyed massive circulation boosts after the News of the World closure – the People to more than 800,000 and the Daily Star Sunday to more than 700,000.

Following the launch of the Sunday edition of the Sun in late February both titles suffered a significant sales slump, with the People's circulation falling below the Daily Star Sunday's in the process.

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